Question

if x = 2+ root 3 , then find the value of x² + 1/x²

Answer 1

Hello Mate!

$x = 2 + \sqrt{3} \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ = \frac{2 - \sqrt{3} }{4 - 3} = 2 - \sqrt{3} \\ {x}^{2} = {(2 + \sqrt{3} )}^{2} \\ = 4 + 3 + 4 \sqrt{3} \\ = 7 + 4 \sqrt{3} \\ \frac{1}{ {x}^{2} } = {(2 - \sqrt{3} )}^{2} \\ = 4 + 3 - 4 \sqrt{3} \\ = 7 - 4 \sqrt{3} \\ {x}^{2} + \frac{1}{ {x}^{2} } \\ 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3 } \\ = 14$
Hope it helps☺!✌

Answer 2

(2+√3)(2+√3)+1/(2+√3)(2+√3)
4+3+4√3+1/4+3+4√3
7+4√3+1/7+4√3
49+48+56√3+1/7+4√3
98+56√3/7+4√3
98+96.88/7+6.92
194.88/13.92
=14